Discussion of “Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem”

We commend the authors of [1] for application of an interesting optimization methodology, i.e., adaptive robust optimization to solve the security constrained unit commitment problem (SCUC). They present a two-stage adaptive robust unit commitment model for SCUC considering the uncertainty of nodal net injection in power system. The two-stage adaptive model is intended to obtain the first-stage unit commitment (UC) decision and the second-stage dispatch decision to become robust against all uncertain nodal net injection realizations. In [1], the first-stage UC decision is a vector of binary variables, which includes the on/off and start-up/shut-down status of each generation unit for each time interval of the commitment period. The second-stage dispatch decision is a vector of continuous variables, composed of the generation output, load consumption levels, resource reserve levels, and power flows in the transmission network for each time interval. In addition, the authors have pointed out that generation output, resource reserve levels, and power flow take positive sign, whereas load consumption levels take negative sign. Therefore, the discusser has certain doubt about [1, (8)]. If each element of the second-stage dispatch decision can take any real number, then equation (8) is of no question. However, actually, each element of takes either positive or negative sign as the authors pointed out. As a result, the discusser doubts about equation (8). This question is quite important because the dual of the dispatch problem, (8), is the mathematical basis of the proposed two-stage adaptive robust UC model.